|
Search: id:A050470
|
|
|
| A050470 |
|
Sum_{d|n, n/d == 1 mod 4} d^2 - Sum_{d|n, n/d == 3 mod 4} d^2. |
|
+0
7
|
|
| 1, 4, 8, 16, 26, 32, 48, 64, 73, 104, 120, 128, 170, 192, 208, 256, 290, 292, 360, 416, 384, 480, 528, 512, 651, 680, 656, 768, 842, 832, 960, 1024, 960, 1160, 1248, 1168, 1370, 1440, 1360, 1664, 1682, 1536, 1848, 1920, 1898, 2112, 2208, 2048, 2353, 2604
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Multiplicative because it is the Dirichlet convolution of A000290 = n^2 and A101455 = [1 0 -1 0 1 0 -1 ...], which are both multiplicative. Christian G. Bower (bowerc(AT)usa.net) May 17, 2005.
|
|
FORMULA
|
G.f.: Sum_{n>=1} n^2*x^n/(1+x^(2*n)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 16 2002
Euler transform of period 4 sequence [4, -2, 4, -6, ...]. - Michael Somos, Aug 08 2005
Expansion of eta(q^2)^6*eta(q^4)^4/eta(q)^4 in powers of q. - Michael Somos, Aug 08 2005
G.f.: x Product_{k>0} (1+x^k)^4*(1-x^(2k))^2*(1-x^(4k))^4 . - Michael Somos, Aug 08 2005
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u*w*(u-8*v)*(v-4*w)-v^2*(v-8*w)^2 . - Michael Somos, Aug 08 2005
G.f.: Sum_{k>0} kronecker(-4, k) x^k(1+x^k)/(1-x^k)^3 . - Michael Somos Sep 02 2005
Expansion of phi(q)^2 * psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos Aug 15 2007
G.f. is a period 1 Fourier series which satisfies f(-1/ (4 t)) = (1/2) (t/i)^3 g(t) where q = exp(2 pi i t) and g() is g.f. for A120030.
|
|
EXAMPLE
|
q + 4*q^2 + 8*q^3 + 16*q^4 + 26*q^5 + 32*q^6 + 48*q^7 + 64*q^8 + ...
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d^2*(n/d%2)*(-1)^(n/d\2)))
|
|
CROSSREFS
|
Cf. A050469, A050471, A050468.
Sequence in context: A003451 A013934 A167189 this_sequence A138501 A096296 A068936
Adjacent sequences: A050467 A050468 A050469 this_sequence A050471 A050472 A050473
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
|
|
|
Search completed in 0.002 seconds
|
